How do we know what the integral of $\sin (x)$ is?
Since I started more or less formally learning the foundations of calculus, I naturally came across the Riemann definition of the integral. At first I con...
04 Apr 2026 1 READS
Find the arclength of the curve defined by $r(t)=i+9t^2j+t^3k$ for $0 \leq t \leq \sqrt28$.
First I found $r'(t)=\langle 1,18t^2,3t^2\rangle$ and so the magnitude of $r'(t)= \sqrt{1+(18t)^2+(3t^2)^2}$ thus the integral from $0$ to $\sqr...
04 Apr 2026 1 READS
Proving the Splitting Lemma on pg.147 in AT.
The Lemma and a sketch of its proof are given below: My questions are: 1- why the diagram that must be commutative looks specifically like this? My profes...
04 Apr 2026 1 READS
Matrix addition/multiplication with different sizes
I have the following two matrices: $$A=\begin{pmatrix}1 & -2\\3 & 1\end{pmatrix}\text{ and }B=\begin{pmatrix}1 & 3 & 2\\-1 & 0 & 2...
04 Apr 2026 1 READS
CPU Usage : Top and mpstat shows different results
top %Cpu(s): 10.9 us, 3.1 sy, 0.0 ni, 85.2 id, 0.2 wa, 0.0 hi, 0.7 si, 0.0 st 31426 www-data 20 0 309088 21276 14600 S 22.3 0.1 0:07.36 php-fpm: pool www ...
04 Apr 2026 1 READS
Definition of an angle vs measurement of an angle
The definition of an angle in Euclidean geometry is given as follows: Angle. Definition: A shape, formed by two lines or rays diverging from a common poin...
04 Apr 2026 1 READS
Finding Anchor and Reference Point of a Cube Root Function.
My brother sent me a question from his Pre-Calculus Study Guide. I have been studying math for $4$ years and don't ever recall seeing a question like...
04 Apr 2026 1 READS
$\lim_{x\to 0^+} (\sin x)^ {\tan x}$
I have stumbled on this question in one of my problem sets from Cal I and I'm not sure how to proceed after the last step. $$\lim_{x\to 0^+} (\sin x)...
04 Apr 2026 1 READS
Alsamixer returns "cannot open mixer: No such file or directory"
alsamixer returns: cannot open mixer: No such file or directory after sudo apt install jack sudo lspci -v | grep -i audio returns 00:1b.0 Audio device: In...
04 Apr 2026 1 READS
Fibocom L850-GL installation on Ubuntu 18.04
I have a new gen 6 X1 carbon with a 4G connection. But, unfortunately, I could not install it in Ubuntu 18.04. I appreciate if anybody can help to install...
04 Apr 2026 1 READS
